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LuckyWell [14K]
3 years ago
10

Mr. Abernathy purchased a selection of wrenches for his shop. The total cost was $78. He bought the same number of $1.50 and $2.

50 wrenches, and half that many $4 wrenches. The number of $3 wrenches was one more than the number of $4 wrenches. How many of each did he purchase?
Mathematics
1 answer:
Over [174]3 years ago
6 0
78 = 1.50x + 2.50x + 4(x/2)) + 3((x/2) + 1))
78 = 4x + 4(x/2) + 3((x/2)+1)
78 = 4x + 2x + (3(x/2) + 3)
78 = 6x + 1.5x + 3
75 = 7.5x
10 = x
Mr. Abernathy bought 10 wrenches at $1.50, 10 wrenches at $2.50, 5 wrenches at $4, and 6 wrenches at $3.
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Evaluate the following expression when x = -5 and y = 25.
kykrilka [37]

Answer:

<u>The correct answer is A. 3,120.</u>

Step-by-step explanation:

Let's solve the expression for x = -5 and y = 25, this way:

(5|x| - y³)/x

Replacing x and y, we have:

(5 * 5 - 25³)/-5 (Absolute value of -5 is 5 in the numerator but we keep it without changes in the denominator)

(25 - 15,625)/-5

-15,600/-5

3,120

<u>The correct answer is A. 3,120.</u>

3 0
3 years ago
If x2 + y2=6 , xy = 5 , then (X + y)2? <br><br><br><br>​
VARVARA [1.3K]

Answer:

(x + y)² =16

Step-by-step explanation:

hello :

(x + y)² = x²+y²+2xy   and : x²+y² = 6     xy = 5

(x + y)² = 6+2(5)

(x + y)² =16    

3 0
2 years ago
HAVE A NICE DAY <br> WILL GIVE BRAINLST :)
Arturiano [62]

Answer:

DEF = 103

Step-by-step explanation:

brainlyist pls

4 0
3 years ago
No link or bot answer the question
sasho [114]

Answer:

c. Rational

because → whole numbers are positive and Starts from 0 so not whole number

Integers can be negative and positive

Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, . 09, and 5,643.1.

Irrational number that cannot be written in p/q

but -2.4 written in p/q = -24/100

<h3>so c. Rational Number is correct</h3>
3 0
2 years ago
A line tangent to the curve f(x)=1/(2^2x) at the point (a, f(a)) has a slope of -1. What is the x-intercept of this tangent?
kirza4 [7]

Answer:

x-intercept = 0.956

Step-by-step explanation:

You have the function f(x) given by:

f(x)=\frac{1}{2^{2x}}   (1)

Furthermore you have that at the point (a,f(a)) the tangent line to that point has a slope of -1.

You first derivative the function f(x):

\frac{df}{dx}=\frac{d}{dx}[\frac{1}{2^{2x}}]  (2)

To solve this derivative you use the following derivative formula:

\frac{d}{dx}b^u=b^ulnb\frac{du}{dx}

For the derivative in (2) you have that b=2 and u=2x. You use the last expression in (2) and you obtain:

\frac{d}{dx}[2^{-2x}]=2^{-2x}(ln2)(-2)

You equal the last result to the value of the slope of the tangent line, because the derivative of a function is also its slope.

-2(ln2)2^{-2x}=-1

Next, from the last equation you can calculate the value of "a", by doing x=a. Furhtermore, by applying properties of logarithms you obtain:

-2(ln2)2^{-2a}=-1 \\\\2^{2a}=2(ln2)=1.386\\\\log_22^{2a}=log_2(1.386)\\\\2a=\frac{log(1.386)}{log(2)}\\\\a=0.235

With this value you calculate f(a):

f(a)=\frac{1}{2^{2(0.235)}}=0.721

Next, you use the general equation of line:

y-y_o=m(x-x_o)

for xo = a = 0.235 and yo = f(a) = 0.721:

y-0.721=(-1)(x-0.235)\\\\y=-x+0.956

The last is the equation of the tangent line at the point (a,f(a)).

Finally, to find the x-intercept you equal the function y to zero and calculate x:

0=-x+0.956\\\\x=0.956

hence, the x-intercept of the tangent line is 0.956

5 0
3 years ago
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